Looking at the blockchain explorer it looks like there are 3 slots every minute, e.g. slot times are 20 seconds. However the constants file specifies 15-second slot times.
What is the slot time? Why is the Github repo seemingly out of sync with the block explorer?
20 seconds. Afaik, it is specified in the genesis block, as described here: https://github.com/input-output-hk/cardano-sl/blob/master/scripts/prepare-genesis/README.md
"slotDuration": "20000"
"slotDuration" - slot duration, in microseconds
Because your link is pointing to a commit from May 29, 2017 and to a file that does not even exist anymore 
Cardano’s mainnet was bootstrapped from the mainnet-genesis.json, which is in accord with the README that @vantuz-subhuman pointed out, and also the mainnet processing the slots in every 20secs. 